I'm sure that everyone has heared of a "Beta". A feature which allows specially selected players to play and test a game/expansion before it is released for the public gamers. Well, an "Alpha" version is exactly the same, but it has features and textures that are unfinished on purpose, some places which actually have been finished look different (Like the Undercity, Orgrimmar and Ironforge in WoW Alpha), and it's used to test some special features which might be released in the Beta or finished WoW.
An "Alpha" version of a game is also mainly tested by the game designers instead of the gamers, but it can be accessed by hacking it, or in this case, finding a Live server.
Of course, the "Alpha" version can no longer be accessed, because the game is finished by now.

Anyways, here's a movie which shows some parts of WoW: Alpha, and some of the features that have been removed in the Beta. Enjoy!